How to get blender to write the correct diffuse color (Kd) in exported .mtl files?
Since 3D file formats such as .obj/.mtl cannot represent complex node graphs, the .obj exporter add-on only considers the Principled BSDF when creating the file. All other shader nodes are ignored. This is documented in Blender's manual.

I can't reproduce the problem with Kd having different colors in 2.81a. In case previous Blender versions applied the view transform on the scene linear RGB value from the color picker before writing the .mtl, try to temporarily set the View Transform to Raw in the Color Management panel.